A team of researchers from across the U.S. has solved the Kadison-Singer conjecture, a hypothesis about the mathematical nature of the way physicists can perform measurements in quantum systems. The researchers also say they made a breakthrough in a subfield of mathematics called graph theory, which deals with mathematical objects that can be used in a wide range of applications. After years of trying and failing to prove the Kadison-Singer conjecture, the researchers turned their attention to the graph theory problem. The researchers developed a method to solve the graph theory problem, and found they were able to use it to help solve the Kadison-Singer conjecture. “The purpose of these papers is to introduce a new technique to understand situations that mathematics previously could not understand,” says Yale University researcher Adam Marcus. Yale professor Dan Spielman, in the process of working on the proof, wrote software that proved many smaller conjectures, each of which suggested Kadison-Singer is true. Spielman also constructed programs that would come up with random matrices on which to test the mini conjectures. “We tested them a lot [with computer programs], but not only could we not find counter-examples, but the conjectures looked really tight,” Spielman says.